Week 29.01.2023 – 04.02.2023

These lectures aim to provide a self-contained introduction to the modern conformal bootstrap method. The study of conformal field theory (CFT) will first be motivated and the “old” way of studying CFTs as endpoints of RG flows will be explained. The set of ideas necessary to understand the conformal bootstrap method will then be introduced, and both analytic and numerical implementations of the conformal bootstrap method will be discussed.

Please visit https://lonti.weebly.com/spring-2023-series.html for more information.

Speaker: Lassina Dembele, 14:00-14:20

Title: Quaternionic Hermitian lattices and applications.

Abstract: In this short presentation, I will report on some work on quaternionic Hermitian lattices and discuss how these lattices relate to automorphic forms.

Speaker: Igor Wigman, 14:30-14:50

Title: Around Gauss circle problem: Hardy's conjecture and the distribution of lattice points near circles

Abstract: This talk is based on a joint work with Steve Lester.

We review the Gauss circle problem, and Hardy's conjecture regarding the order of magnitude of the remainder term. It is attempted to rigorously formulate the folklore heuristics behind Hardy's conjecture. Some weaker forms of the likely statement are proved to support it.

In this work we provide the best estimate for the functional coefficient in a linear model with functional response and multivariate predictor, exploiting fully the information provided by both functions and derivatives. The model includes possible random effects due to repeated measurements. We also study the theory of optimal design of experiments when functional observations occur. We define different optimality criteria for the estimate of the functional coefficient. We provide a strong theoretical foundation to prove that the computation of these optimal designs, in the case of linear models, is the same as in the classical theory, but different interpretations need to be given.